Question

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made:
(i) The quantity of S sold was twice that of T.
(ii) The quantity of R sold was thrice that of T.
(iii) The quantity of Q sold was four times that of T.

Product	P	Q	R	S	T
Unit selling price (Rs.)	100	50	40	60	60

What is the quantity of product P sold on that day?

• A. 40
• B. 50
• C. 60
• D. 70

Hint:

Write one equation for the total number of items (250) and one for the total revenue (250 times Rs. 60), using T as the base quantity.

Answer 1

The Correct Option is B

Step 1: Set up variables using the given ratios.
Let the quantity of T sold be \(t\). From the observations, the quantity of S is \(2t\), the quantity of R is \(3t\), and the quantity of Q is \(4t\). Let the quantity of P sold be \(p\).

Step 2: Write the total quantity equation.
The total number of items sold is 250, so
\[ p+4t+3t+2t+t=250 \] \[ p+10t=250 \]
Step 3: Write the total revenue equation.
The average selling price is Rs. 60 for 250 items, so the total revenue is
\[ 250\times60=15000 \] Using the unit prices from the table, the total revenue is also
\[ 100p+50(4t)+40(3t)+60(2t)+60(t)=15000 \] \[ 100p+200t+120t+120t+60t=15000 \] \[ 100p+500t=15000 \]
Step 4: Solve the two equations together.
From Step 2, \(p=250-10t\). Substitute this into the revenue equation:
\[ 100(250-10t)+500t=15000 \] \[ 25000-1000t+500t=15000 \] \[ 25000-500t=15000 \] \[ 500t=10000 \] \[ t=20 \]
Step 5: Find the quantity of P.
\[ p=250-10t=250-10(20)=250-200=50 \]
Step 6: Final Answer.
The quantity of product P sold that day is 50 units.
\[ \boxed{50} \]